Citizenship through U.S. citizen parents under the Child Citizenship Act, Form N-600 applications, and consular reports of birth abroad.
A child born in the U.S. to a foreign diplomat is not a citizen at birth. A passport isn't proof to USCIS. Get an N-600 before you try to petition for family.
A child born abroad to a U.S. citizen is likely already a citizen. File a CRBA to document it; an I-130 wastes the fee and years of waiting.
A stalled N-600 and a spouse's overdue N-400 can go into a single federal suit. The 120-day rule and the APA are what move each one.